Henry P. McKean Jr. Selecta PDF
Preview Henry P. McKean Jr. Selecta
Contemporary Mathematicians F. Alberto Grünbaum Pierre van Moerbeke Victor H. Moll Editors Henry P. McKean Jr. Selecta Contemporary Mathematicians Joseph P.S. Kung Editor Moreinformationaboutthisseriesathttp://www.springer.com/series/4817 F. Alberto Gru¨nbaum • Pierre van Moerbeke • Victor H. Moll Editors Henry P. McKean Jr. Selecta Editors F. Alberto Gru¨nbaum Pierre van Moerbeke Department of Mathematics Institut deRechercheen Math´ematique at University of California Physique Berkeley Universit´ecatholique de Louvain California, USA Louvain-la-Neuve,Belgium Department of Mathematics Brandeis University Waltham Massachusetts, USA Victor H. Moll Tulane University New Orleans Louisiana, USA ContemporaryMathematicians ISBN978-3-319-22236-3 ISBN978-3-319-22237-0 (eBook) DOI10.1007/978-3-319-22237-0 LibraryofCongressControlNumber:2015960201 SpringerChamHeidelbergNewYorkDordrechtLondon ©SpringerInternationalPublishingSwitzerland2015 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewhole orpart ofthematerial isconcerned, specifically the rights oftranslation, reprinting, reuse of illustrations,recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway, andtransmissionorinformationstorageandretrieval,electronicadaptation,computersoftware, orbysimilarordissimilarmethodologynowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthis publication does not imply, even in the absence of a specific statement, that such names are exemptfromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. 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Printedonacid-freepaper SpringerInternationalPublishingAGSwitzerlandispartofSpringerScience+Business Media (www.birkhauser-science.com) To my teachers Will Feller, Kiyoshi Ito, Mark Kac, Norman Levinson and Gretchen Warren Contents 1 PersonalRecollections ............................... 1 2 MyDebttoHenryP.McKeanJr...................... 11 3 HenryP.McKeanJr.andIntegrableSystems ......... 15 4 SomeComments..................................... 31 5 SomeWordsfromThreeStudents .................... 49 6 CurvatureandtheEigenvaluesoftheLaplacian ....... 55 7 Hill’sOperatorandHyperellipticFunctionTheory inthePresenceofInfinitelyManyBranchPoints ...... 79 8 BookReviews:RiemannSurfacesofInfiniteGenus byJ.Feldman,H.Kno¨rrer,andE.Trubowitz.CRM Monographseries.Vol.20,Amer.Math.Soc........... 141 9 FredholmDeterminantsandtheCamassa-Holm Hierarchy ........................................... 151 10 BreakdownoftheCamassa-HolmEquation ........... 191 11 RationalTheoryofWarrantPricing .................. 197 12 GeometryofKdV(1):AdditionandtheUnimodular SpectralClasses ..................................... 235 13 WeightedTrigonometricalApproximationonR1 withApplicationtotheGermFieldofaStationary GaussianNoise ...................................... 257 14 BrownianLocalTimes ............................... 295 15 BrownianMotionsonaHalfLine ..................... 313 16 TheSpectrumofHill’sEquation...................... 363 VII Personal Recollections 1 Henry P. McKean Jr.1 1.1. Norman Levinson his unobtrusive, remarkably effective admin- istrative style, the way he seemed to run the Thinking of Norman Levinson, I remem- department with the back of his hand, and, ber how much I learned from him as a very on the personal side, his patience and gentle young and inexperienced person, and how encouragement. much I found to admire, both in his math- He wasshy.Fagisaid:“Norman,he’ster- ematical work and in himself, as a man. rible. He never wants to go out. He’s afraid Lookingback,his choiceofmathematical he’ll meet somebody he doesn’t know.” I was questions seems memorable enough: mostly shy,too,butslowlywegottoknoweachother closetoapplications,richintheirdetails,sug- alittle, comingfromasdifferentbackgrounds gestive of general phenomena, as in the won- as you could imagine, and I thought myself derful papers on the forced vander Pol equa- luckywhenhetoldmebitsabouthisearlylife. tion, etc. foreshadowing the current vogue of He said: “We were very poor, but we didn’t attractors, chaos, and all that. think of ourselves as poor.” I take the liberty What I could better appreciate then was to transpose that and to say he was a rich his mastery of the kind of hard analysis such man in his particular way, spreading about questions require, the kind in which every his riches quietly, with an open hand. equality costs you two opposing inequalities. Henry McKean, New York, May 1997. When we got stuck, working together, he’d always take an example, and he’d estimate 1.2. Will Feller things with an understanding and a speed Will Feller was born in Zagreb, Yu- that impressed me equally, and soon we’d goslavia on July 7, 1906, the ninth of 12 be back on solid ground. It was excitingly children of a well to-do family. They named easy, Norman doing all the hard work, as I him Willy in the then popular German style. understood later.Gap and Density Theorems This changed to William upon his coming (Chap.8,vol.2)andtheextraordinarypapers here (1939), but everybody called him plain onRiemann’s zeta function (Chap.11, vol.2) Will.HisearlystudiescalledhimfromZagreb is where you can see this expertise at its (1923–1925)to Gottingen (1925–1928)where best. he got his degree in 1926, aged 20! Then Other lessons I was not so ready to di- to Kiel as Privatdozent (1928–1933). Nazi gest though happy to benefit from. I mean times: Will taught a class on the new ideas in probability of Kolmogorov, etc., attended, 1Courant Institute, New York University, by chance, by a person of some importance NewYork,NY,USA,[email protected]. in the SS. One day, this person and some 1 © Springer International Publishing Switzerland 2015 F.A. Gru¨nbaum et al. (eds.), Henry P. McKean Jr. Selecta, Contemporary Mathematicians, DOI 10.1007/978-3-319-22237-0 1 2 1.PERSONALRECOLLECTIONS Figure 1.1. Henry P. McKean Jr. two or three of his men present themselves I think it is fair to say that Kolmogorov, at Will’s apartment. Will lets them in in fear Paul L´evy, and Will made probability an and trembling, whereupon the boss says how honest woman. They are the people chiefly much he loves Will’s lectures and if there responsible for its rise from a not quite re- is somebody Will would like them to beat spectable rule of thumb to the ubiquitous, up, just to say the word. A courtesy call I precise, intuitively appealing subject it is to- suppose. Will declined this civility and after day. I think that, of the three, Will had a subsequent refusal to sign a Nazi oath, the wider view. He understood Kolmogorov’s packed his bags for Copenhagen where he mostly analytical way and also Paul L´evy’s stayed a year (1933). Then to Stockholm way with sample paths, and was a master (1934–1939), Providence (1939–1944), Ithaca of both, as can best be seen in his splendid (1945–1950), and Princeton (1950–) which is book, An Introduction to Probability Theory where I first knew him (1953). He died, with (JohnWiley&Sons,1950)anditssubsequent difficulty, in New York on January 14, 1970, amplifications and revisions (1957/1968 and aged 63. 1966/1971). Here you can see him endlessly
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